Answer this question

P is the point with coordinates (3, 1)

earnstyle [38]

Answer:

c will be the answer mark me brainliest

3 0

3 years ago

What would the equation be ?

Vikentia [17]

Answer:

y = 4/5x-18/5

Step-by-step explanation:

First we find the slope from the given points (-3,-6) (2,-2)

m = (y2-y1)/(x2-x1)

m = (-2 - -6)/(2 - -3)

(-2+6)/( 2+3)

4/5

The slope intercept form of an equation is

y = mx +b where m is the slope and b is the y intercept

y = 4/5 x +b

Substitute a point into the equation to find b

-6= 4/5(-3) +b

-6= -12/5 +b

Add 12/5 to each side

-6 +12/5 = -12/5 +12/5 +b

Get a common denominator

-30/5 + 12/5 = b

-18/5 =b

The equation is

y = 4/5x-18/5

4 0

3 years ago

) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

PLS HELP I WILL GIVE BRAINIEST JUST PLSSS

Luden [163]

Answer:

bc it has the same value

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

!!!!!!!!!!!!!!!! URGENT !!!!!!!!!!!!!!!!!! 1.2 Learning Checkpoint

Grace [21]

Answer: Try to figure it out first. If you can't, then you haven't learned the material and you won't be able to understand subsequent lessons.

Step-by-step explanation:

Question 1 checks that you know several things:

● Point (5,8) means x=5 and y=8.

● Which number is the y intercept in equation y = m x + b.

m is NOT the y intercept.

b IS the y intercept.

Guess which is the slope...

● The y intercept is value of y when x is zero. But m times zero is zero, no matter what m is, so m can't be the y intercept. On the other hand, m x + b evaluates to b when x is zero.

● The meaning of an inequality and how it is graphed:

A solid line means the line is included in the graph (≤ or ≥).

A dotted line means the line is not included (< or >).

The shaded area indicates points in that area are in the solution set of the inequality.

● To see if point (A,B) is in the solution set, substitute A for x and B for y, and see if the result is true.

Say (A,B) = (5,6), and the statement is y < 2x + 3. You substitute A (5) for x and evaluate the right hand side to a number (13), and substitute B (6) for y on the left hand side to give a statement about two numbers: 6 < 13. If the statement is true, then (A,B) is in the solution set.

Then the region containing (A,B) will be shaded (inequality), or a solid line (equation).

Question 2 tries to see if you realize you can't draw a line between two points without first plotting both points.

Question 3 checks to see if you know how to tell if an equation matches a line on graph paper. You can look at the line, find the y intercept (b) and the slope (m), and look for an equation y = m x + b.

For instance, the red line crosses the y axis at (0,4), x = 0 (always true for a y intercept), and y = 4. So the equation for the red line must be

y = m x + 4. If you substitute (0,4), you get 4 = m × 0 + 4 = 4, a true statement.

You can figure the slope of the red line as m = rise/run. The answer is m=2, so the equation is y = 2x+4.

Or you can just check all of the choices. Takes longer but you don't have to know how to find slope.

But after doing this (or even without doing it), you check to see if a few points from the line make the equation true. The red line includes (-4,-4). So check -4 = 2(-4) + 4. Since -8+4 is -4, the result is true. Also check (0,4) and (-2,0) because they are easy to do. 4 = 2(0)+4, true, and 0 = 2(-2) + 4, true. y = 2x + 4 is the equation of the red line.

If the check fails, then either you don't know how to read the slope and y intercept, or else you don't know how to substitute x and y into the equation.

Another way to eliminate incorrect choices quickly is to substitute (-3,-2), x = -3, y = -2, into each pair. If either equation evaluates to false, eliminate that choice. But that might not eliminate all but one choice, so you need to test all of them.

The last question checks to see if you can figure out which axis is x and which is y, and if you know (-3,-2) means x=-3, y=-2, and not x=-2, y=-3.

7 0

3 years ago